Layered transition-metal dichalcogenides are proposed as building blocks for van der Waals heterostructures due to their graphenelike two-dimensional structure. For this purpose, a magnetic semiconductor could represent an invaluable component for various spintronics and topotronics devices. Here, we combine different local magnetic probe spectroscopies with angle-resolved photoemission and density-functional theory calculations to show that 2H-MoTe₂ is on the verge of becoming magnetic. Our results present clear evidence that the magnetism can be "switched on" by a hydrogenlike impurity. We also show that this magnetic state survives up to the free surface region, demonstrating the material’s potential applicability as a magnetic component for thin-film heterostructures.